Description
A brine solution containing 3kg of salt per gallon flows at a constant rate of 20gal/minute into a tank that holds 400 gallons of pure water. The mixture in the tank is kept well stirred and flows out of the tank at the rate of 25gal/min.
a) find the mass of salt in the tank at time t
b) find the concentration of salt in the tank when there is 200 gallons of solution
c)When will the tank be empty?
Explanation & Answer
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(a) rate in = 3kg/gal * 20gal/min = 60 kg/min
dS/dt = rate in - rate out
dS/dt = 60 - (25S)/(400-5t)
ln(S) = 60t + 5Sln(t-80) + constant
S = e^(60t + 5ln(t-80))
(b) V=200 at t = 40 minutes, so C = 10kg/gal
(c) you lose 5 gal/min, so you will be empty after 400/5 = 80 minutes = 1 hour and 20 minutes
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